Problem: Good job! Now that Heidi is able to distinguish between Poisson and uniform distributions, she is in a good position to actually estimate the populations.

Can you help Heidi estimate each village's population?

Input

Same as the easy version.

Output

Output one line per village, in the same order as provided in the input, containing your (integer) population estimate.

Your answer is considered correct if it is an integer that falls into the interval <image>, where P is the real population of the village, used to create the distribution (either Poisson or uniform) from which the marmots drew their answers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
//debug
#ifdef grief
#define debug(...) do{\
	fprintf(stderr , "%s - %d : (%s) = " , __PRETTY_FUNCTION__ , __LINE__ , #__VA_ARGS__ );\
	_DO(__VA_ARGS__);\
}while(0)
template<typename I> 				void _DO(I&&x){	cerr<<x<<endl;	}
template<typename I,typename...T>	void _DO(I&&x,T&&...tail){	cerr<<x<<" , ";	_DO(tail...);	}
template<typename _a,typename _b> 	ostream& operator << (ostream &_s,const pair<_a,_b> &_p)
{	return _s<<'('<<_p.first<<','<<_p.second<<')';	}
#define IOS
#else
#define debug(...)
#define IOS do{ios_base::sync_with_stdio(0); cin.tie(0);}while(0);
#endif
//type
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef priority_queue<pll,vector<pll>,greater<pll> > heap;
//macro
#define SZ(x) ((ll)(x).size())
#define ALL(x) (x).begin(),(x).end()
#define F first
#define S second
#define pb push_back
#define eb emplace_back
#define stp setprecision(30)<<fixed
const ll INF=0x3f3f3f3f3f3f3f3f;
const ll MAX=1e5+5,Mlg=__lg(MAX)+2;
const ll MOD=1e9+7;
//}}}
double arr[260];
int main(){
	IOS
	int n;	cin>>n;
	while(n--){
		double sum=0;
	    int ma = 0;
		for(int i=0;i<250;i++){
			cin>>arr[i];
			sum+=arr[i];
			ma = max(ma, (int)arr[i]);
		}
		double mu=sum/250;
// 		cout << min(max(int(mu + 0.5), 10), 1000) << '\n';
		double var=0;
		for(int i=0;i<250;i++)
			var+=(arr[i]-mu)*(arr[i]-mu);
		var/=250;
		if(abs(mu-var) < abs(var-mu*mu/3 ))  {
// 			cout<<"poisson\n";
            cout << min(max(int(mu + 0.5), 10), 1000) << '\n';
		}
		else{
		    cout << ma / 2 << '\n';
		}
	}
	return 0;
}